Unit 3: Introduction to Trigonometry

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Unit 3 Introduction to Trigonometry

• LG 3-1 Angle Measures (quiz tomorrow)
• LG 3-2 THE Unit Circle (quiz Thursday)
• LG 3-3 Evaluating Trig Functions
• LG 3-4 Arc Length

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Consider a circle, centered at the origin with 2
rays extending from the center.
One ray is fixed along the positive x-axis
The other can rotate about the center

• These rays form an angle. The fixed ray is called
  the initial side of the angle.
• The other side is called the terminal side.
• Any angle with vertex at the origin and initial
  side along the positive x-axis is in standard
  position.

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As the terminal side is rotated counterclockwise,
the measure of the angle that is formed
increases.
30o
135o
210o
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The rotation of the terminal side may include 1
or more complete revolutions about the center.
The measurement representing 1 complete
revolution is 360o
1 revolution 360o
2 revolutions 720o
1 revolution 60o 420o
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Angles that differ by one or more complete
revolutions are called coterminal angles.

• For example 74o, 434o, and 794o are all
  coterminal angles. Why?
• Think of at least 2 coterminal angles for 105o

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The terminal side of an angle can also rotate
clockwise. A negative number is used to denote
these angle measures.
-45o
-150o
-420o
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Suppose these angles are in standard position.
Place each angle in the quadrant that contains
its terminal side.
245o 275o 440o -94o
397o -240o 178o 945o
800o -32o 300o -210o
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90o
-240o
397o
-210o
800o
440o
First, label the points where the circle
intersects the axes.
How would these angles change if they opened
clockwise?
180o
0o
360o
245o
-32o
198o
-94o
300o
275o
945o
270o
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A unit other than degrees is also used to
describe the measure of an angle. It is called
the radian.

• Suppose there is a circle with radius of 1
  centered at the origin. Its called the Unit
  Circle (more tomorrow!)
• Form an angle in standard position so that it
  intercepts an arc whose length is one unit.
• The angle made is given the measurement of 1
  radian.

Approximately 6.28 of these slices can fit all
the way around the circle
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So 2?360o

• You will convert degrees to radians and vice
  versa by using this conversion